MA19.5.3
Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and $\frac{1}{10}$ of what it represents in the place to its left.
Using models and quantitative reasoning, explain that in a multi-digit number, including decimals, a digit in any place represents ten times what it represents in the place to its right and $\frac{1}{10}$ of what it represents in the place to its left.
Unpacked Content
UP:MA19.5.3
Vocabulary
- Digit
- Decimal
- Decimal point
- Thousandths
- Hundredths
- Tenths
- Base-ten
- Expanded form
- Place value
- Power of 10
- Factor
- Base
- Exponent
- Product
Knowledge
Students know:
- Each place value position represents 10 times what it represents in the place to its right.
Example: In 433, the underlined 3 represents 3 tens and has a value of 30 which is ten times the value of the 3 ones to its right. - Place value understanding is extended to apply reasoning that a place value position represents 1/10 of what it represents in the place value to its left.
Example: In 433, the underlined 3 represents 3 ones and has a value of 3 which is one-tenth of the value of the 3 tens or 30 to its left. - A given number multiplied by a power of 10 shifts the digits in the given number one place value greater (to the left) for each factor of 10.-A given number divided by a power of 10 shifts the digits in the given number one-tenth of the value (to the right) for each factor of 10.
Skills
Students are able to:
- Reason and explain the relationship between two successive place values.
- Explain patterns of zeros of the product when multiplying by powers of 10.
- Explain patterns in placement of decimals when multiplying or dividing by power of 10.
- Write powers of 10 using exponential notation.
Understanding
Students understand that:
- The relationship of adjacent places values in the base ten system extend beyond whole numbers to decimal values.
- Multiplying or dividing by a power of 10 shifts the digits in a whole number or decimal that many places to the left or right respectively.
